dolfinx.geometry
Methods for geometric searches and operations.
Functions

Create a bounding box tree for use in collision detection. 

Compute closest mesh entity to a point. 

From a mesh, find which cells collide with a set of points. 

Compute collisions between points and leaf bounding boxes. 

Compute all collisions between two bounding box trees. 

Compute the distance between two convex bodies p and q, each defined by a set of points. 

Create a bounding box tree for the midpoints of a subset of entities. 

Compute the squared distance between a point and a mesh entity. 
Classes

Bounding box trees used in collision detection. 
 class dolfinx.geometry.BoundingBoxTree(tree)[source]
Bases:
object
Bounding box trees used in collision detection.
Wrap a C++ BoundingBoxTree.
Note
 This initializer should not be used in user code. Use
bb_tree
.
 create_global_tree(comm) BoundingBoxTree [source]
 get_bbox(i) ndarray[Any, dtype[floating]] [source]
Get lower and upper corners of the ith bounding box.
 Parameters:
i – Index of the box.
 Returns:
The ‘lower’ and ‘upper’ points of the bounding box. Shape is
(2, 3)
,
 property num_bboxes: int
Number of bounding boxes.
 dolfinx.geometry.bb_tree(mesh: Mesh, dim: int, entities: Optional[npt.NDArray[np.int32]] = None, padding: float = 0.0) BoundingBoxTree [source]
Create a bounding box tree for use in collision detection.
 Parameters:
mesh – The mesh.
dim – Dimension of the mesh entities to build bounding box for.
entities – List of entity indices (local to process). If not supplied, all owned and ghosted entities are used.
padding – Padding for each bounding box.
 Returns:
Bounding box tree.
 dolfinx.geometry.compute_closest_entity(tree: BoundingBoxTree, midpoint_tree: BoundingBoxTree, mesh: Mesh, points: npt.NDArray[np.floating]) npt.NDArray[np.int32] [source]
Compute closest mesh entity to a point.
 Parameters:
tree – bounding box tree for the entities.
midpoint_tree – A bounding box tree with the midpoints of all the mesh entities. This is used to accelerate the search.
mesh – The mesh.
points – The points to check for collision,
shape=(num_points,3)
.
 Returns:
Mesh entity index for each point in
points
. Returns 1 for a point if the bounding box tree is empty.
 dolfinx.geometry.compute_colliding_cells(mesh: Mesh, candidates: AdjacencyList_int32, x: npt.NDArray[np.floating])[source]
From a mesh, find which cells collide with a set of points.
 Parameters:
mesh – The mesh.
candidate_cells – Adjacency list of candidate colliding cells for the ith point in
x
.points – The points to check for collision
shape=(num_points, 3)
,
 Returns:
Adjacency list where the ith node is the list of entities that collide with the ith point.
 dolfinx.geometry.compute_collisions_points(tree: BoundingBoxTree, x: ndarray[Any, dtype[floating]]) AdjacencyList_int32 [source]
Compute collisions between points and leaf bounding boxes.
Bounding boxes can overlap, therefore points can collide with more than one box.
 Parameters:
tree – Bounding box tree.
x – Points (
shape=(num_points, 3)
).
 Returns:
For each point, the bounding box leaves that collide with the point.
 dolfinx.geometry.compute_collisions_trees(tree0: BoundingBoxTree, tree1: BoundingBoxTree) ndarray[Any, dtype[int32]] [source]
Compute all collisions between two bounding box trees.
 Parameters:
tree0 – First bounding box tree.
tree1 – Second bounding box tree.
 Returns:
List of pairs of intersecting box indices from each tree. Shape is
(num_collisions, 2)
.
 dolfinx.geometry.compute_distance_gjk(p: ndarray[Any, dtype[floating]], q: ndarray[Any, dtype[floating]]) ndarray[Any, dtype[floating]] [source]
Compute the distance between two convex bodies p and q, each defined by a set of points.
Uses the Gilbert–Johnson–Keerthi (GJK) distance algorithm.
 Parameters:
p – Body 1 list of points (
shape=(num_points, gdim)
).q – Body 2 list of points (
shape=(num_points, gdim)
).
 Returns:
Shortest vector between the two bodies.
 dolfinx.geometry.create_midpoint_tree(mesh: Mesh, dim: int, entities: npt.NDArray[np.int32]) BoundingBoxTree [source]
Create a bounding box tree for the midpoints of a subset of entities.
 Parameters:
mesh – The mesh.
dim – Topological dimension of the entities.
entities – Indices of mesh entities to include.
 Returns:
Bounding box tree for midpoints of cell entities.
 dolfinx.geometry.squared_distance(mesh: Mesh, dim: int, entities: List[int], points: npt.NDArray[np.floating])[source]
Compute the squared distance between a point and a mesh entity.
The distance is computed between the ith input points and the ith input entity.
 Parameters:
mesh – Mesh containing the entities.
dim – Topological dimension of the mesh entities.
entities – Indices of the mesh entities (local to process).
points – Points to compute the shortest distance from (
shape=(num_points, 3)
).
 Returns:
Squared shortest distance from
points[i]
toentities[i]
.